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Paradis E, Claramunt S, Brown J, Schliep K. Confidence intervals in molecular dating by maximum likelihood. Mol Phylogenet Evol 2023; 178:107652. [PMID: 36306994 DOI: 10.1016/j.ympev.2022.107652] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2022] [Revised: 10/11/2022] [Accepted: 10/19/2022] [Indexed: 11/06/2022]
Abstract
Molecular dating has been widely used to infer the times of past evolutionary events using molecular sequences. This paper describes three bootstrap methods to infer confidence intervals under a penalized likelihood framework. The basic idea is to use data pseudoreplicates to infer uncertainty in the branch lengths of a phylogeny reconstructed with molecular sequences. The three specific bootstrap methods are nonparametric (direct tree bootstrapping), semiparametric (rate smoothing), and parametric (Poisson simulation). Our extensive simulation study showed that the three methods perform generally well under a simple strict clock model of molecular evolution; however, the results were less positive with data simulated using an uncorrelated or a correlated relaxed clock model. Several factors impacted, possibly in interaction, the performance of the confidence intervals. Increasing the number of calibration points had a positive effect, as well as increasing the sequence length or the number of sequences although both latter effects depended on the model of evolution. A case study is presented with a molecular phylogeny of the Felidae (Mammalia: Carnivora). A comparison was made with a Bayesian analysis: the results were very close in terms of confidence intervals and there was no marked tendency for an approach to produce younger or older bounds compared to the other.
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Affiliation(s)
| | - Santiago Claramunt
- Department of Natural History, Royal Ontario Museum, Toronto, ON 5S2C6, Canada
| | - Joseph Brown
- Department of Natural History, Royal Ontario Museum, Toronto, ON 5S2C6, Canada
| | - Klaus Schliep
- Institute of Computational Biotechnology, Technology University Graz, Austria
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Mingrone J, Susko E, Bielawski JP. ModL: exploring and restoring regularity when testing for positive selection. Bioinformatics 2020; 35:2545-2554. [PMID: 30541063 DOI: 10.1093/bioinformatics/bty1019] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2017] [Revised: 11/02/2018] [Accepted: 12/11/2018] [Indexed: 11/14/2022] Open
Abstract
MOTIVATION Likelihood ratio tests are commonly used to test for positive selection acting on proteins. They are usually applied with thresholds for declaring a protein under positive selection determined from a chi-square or mixture of chi-square distributions. Although it is known that such distributions are not strictly justified due to the statistical irregularity of the problem, the hope has been that the resulting tests are conservative and do not lose much power in comparison with the same test using the unknown, correct threshold. We show that commonly used thresholds need not yield conservative tests, but instead give larger than expected Type I error rates. Statistical regularity can be restored by using a modified likelihood ratio test. RESULTS We give theoretical results to prove that, if the number of sites is not too small, the modified likelihood ratio test gives approximately correct Type I error probabilities regardless of the parameter settings of the underlying null hypothesis. Simulations show that modification gives Type I error rates closer to those stated without a loss of power. The simulations also show that parameter estimation for mixture models of codon evolution can be challenging in certain data-generation settings with very different mixing distributions giving nearly identical site pattern distributions unless the number of taxa and tree length are large. Because mixture models are widely used for a variety of problems in molecular evolution, the challenges and general approaches to solving them presented here are applicable in a broader context. AVAILABILITY AND IMPLEMENTATION https://github.com/jehops/codeml_modl. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Joseph Mingrone
- Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada
- Centre for Comparative Genomics and Evolutionary Bioinformatics, Dalhousie University, Halifax, NS, Canada
| | - Edward Susko
- Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada
- Centre for Comparative Genomics and Evolutionary Bioinformatics, Dalhousie University, Halifax, NS, Canada
| | - Joseph P Bielawski
- Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada
- Centre for Comparative Genomics and Evolutionary Bioinformatics, Dalhousie University, Halifax, NS, Canada
- Department of Biology, Dalhousie University, Halifax, NS, Canada
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Laurin-Lemay S, Philippe H, Rodrigue N. Multiple Factors Confounding Phylogenetic Detection of Selection on Codon Usage. Mol Biol Evol 2019; 35:1463-1472. [PMID: 29596640 DOI: 10.1093/molbev/msy047] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Detecting selection on codon usage (CU) is a difficult task, since CU can be shaped by both the mutational process and selective constraints operating at the DNA, RNA, and protein levels. Yang and Nielsen (2008) developed a test (which we call CUYN) for detecting selection on CU using two competing mutation-selection models of codon substitution. The null model assumes that CU is determined by the mutation bias alone, whereas the alternative model assumes that both mutation bias and/or selection act on CU. In applications on mammalian-scale alignments, the CUYN test detects selection on CU for numerous genes. This is surprising, given the small effective population size of mammals, and prompted us to use simulations to evaluate the robustness of the test to model violations. Simulations using a modest level of CpG hypermutability completely mislead the test, with 100% false positives. Surprisingly, a high level of false positives (56.1%) resulted simply from using the HKY mutation-level parameterization within the CUYN test on simulations conducted with a GTR mutation-level parameterization. Finally, by using a crude optimization procedure on a parameter controlling the CpG hypermutability rate, we find that this mutational property could explain a very large part of the observed mammalian CU. Altogether, our work emphasizes the need to evaluate the potential impact of model violations on statistical tests in the field of molecular phylogenetic analysis. The source code of the simulator and the mammalian genes used are available as a GitHub repository (https://github.com/Simonll/LikelihoodFreePhylogenetics.git).
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Affiliation(s)
- Simon Laurin-Lemay
- Department of Biochemistry and Molecular Medicine, Robert-Cedergren Center for Bioinformatics and Genomics, Faculty of Medicine, Université de Montréal, Montréal, QC, Canada
| | - Hervé Philippe
- Department of Biochemistry and Molecular Medicine, Robert-Cedergren Center for Bioinformatics and Genomics, Faculty of Medicine, Université de Montréal, Montréal, QC, Canada.,Centre de Théorisation et de Modélisation de la Biodiversité, Station d'Écologie Théorique et Expérimentale, UMR CNRS 5321, Moulis, Ariège, France
| | - Nicolas Rodrigue
- Department of Biology, Institute of Biochemistry, and School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada
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Dunn KA, Kenney T, Gu H, Bielawski JP. Improved inference of site-specific positive selection under a generalized parametric codon model when there are multinucleotide mutations and multiple nonsynonymous rates. BMC Evol Biol 2019; 19:22. [PMID: 30642241 PMCID: PMC6332903 DOI: 10.1186/s12862-018-1326-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2018] [Accepted: 12/11/2018] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND An excess of nonsynonymous substitutions, over neutrality, is considered evidence of positive Darwinian selection. Inference for proteins often relies on estimation of the nonsynonymous to synonymous ratio (ω = dN/dS) within a codon model. However, to ease computational difficulties, ω is typically estimated assuming an idealized substitution process where (i) all nonsynonymous substitutions have the same rate (regardless of impact on organism fitness) and (ii) instantaneous double and triple (DT) nucleotide mutations have zero probability (despite evidence that they can occur). It follows that estimates of ω represent an imperfect summary of the intensity of selection, and that tests based on the ω > 1 threshold could be negatively impacted. RESULTS We developed a general-purpose parametric (GPP) modelling framework for codons. This novel approach allows specification of all possible instantaneous codon substitutions, including multiple nonsynonymous rates (MNRs) and instantaneous DT nucleotide changes. Existing codon models are specified as special cases of the GPP model. We use GPP models to implement likelihood ratio tests for ω > 1 that accommodate MNRs and DT mutations. Through both simulation and real data analysis, we find that failure to model MNRs and DT mutations reduces power in some cases and inflates false positives in others. False positives under traditional M2a and M8 models were very sensitive to DT changes. This was exacerbated by the choice of frequency parameterization (GY vs. MG), with rates sometimes > 90% under MG. By including MNRs and DT mutations, accuracy and power was greatly improved under the GPP framework. However, we also find that over-parameterized models can perform less well, and this can contribute to degraded performance of LRTs. CONCLUSIONS We suggest GPP models should be used alongside traditional codon models. Further, all codon models should be deployed within an experimental design that includes (i) assessing robustness to model assumptions, and (ii) investigation of non-standard behaviour of MLEs. As the goal of every analysis is to avoid false conclusions, more work is needed on model selection methods that consider both the increase in fit engendered by a model parameter and the degree to which that parameter is affected by un-modelled evolutionary processes.
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Affiliation(s)
- Katherine A. Dunn
- Department of Biology, Dalhousie University, Halifax, Nova Scotia B3H 4J1 Canada
| | - Toby Kenney
- Department of Mathematics & Statistics, Dalhousie University, Halifax, Nova Scotia B3H 4J1 Canada
| | - Hong Gu
- Department of Mathematics & Statistics, Dalhousie University, Halifax, Nova Scotia B3H 4J1 Canada
| | - Joseph P. Bielawski
- Department of Biology, Dalhousie University, Halifax, Nova Scotia B3H 4J1 Canada
- Department of Mathematics & Statistics, Dalhousie University, Halifax, Nova Scotia B3H 4J1 Canada
- Centre Comparative Genomics and Evolutionary Bioinformatics (CGEB) at Dalhousie University, Halifax, Canada
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Looking for Darwin in Genomic Sequences: Validity and Success Depends on the Relationship Between Model and Data. Methods Mol Biol 2019; 1910:399-426. [PMID: 31278672 DOI: 10.1007/978-1-4939-9074-0_13] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Codon substitution models (CSMs) are commonly used to infer the history of natural section for a set of protein-coding sequences, often with the explicit goal of detecting the signature of positive Darwinian selection. However, the validity and success of CSMs used in conjunction with the maximum likelihood (ML) framework is sometimes challenged with claims that the approach might too often support false conclusions. In this chapter, we use a case study approach to identify four legitimate statistical difficulties associated with inference of evolutionary events using CSMs. These include: (1) model misspecification, (2) low information content, (3) the confounding of processes, and (4) phenomenological load, or PL. While past criticisms of CSMs can be connected to these issues, the historical critiques were often misdirected, or overstated, because they failed to recognize that the success of any model-based approach depends on the relationship between model and data. Here, we explore this relationship and provide a candid assessment of the limitations of CSMs to extract historical information from extant sequences. To aid in this assessment, we provide a brief overview of: (1) a more realistic way of thinking about the process of codon evolution framed in terms of population genetic parameters, and (2) a novel presentation of the ML statistical framework. We then divide the development of CSMs into two broad phases of scientific activity and show that the latter phase is characterized by increases in model complexity that can sometimes negatively impact inference of evolutionary mechanisms. Such problems are not yet widely appreciated by the users of CSMs. These problems can be avoided by using a model that is appropriate for the data; but, understanding the relationship between the data and a fitted model is a difficult task. We argue that the only way to properly understand that relationship is to perform in silico experiments using a generating process that can mimic the data as closely as possible. The mutation-selection modeling framework (MutSel) is presented as the basis of such a generating process. We contend that if complex CSMs continue to be developed for testing explicit mechanistic hypotheses, then additional analyses such as those described in here (e.g., penalized LRTs and estimation of PL) will need to be applied alongside the more traditional inferential methods.
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Lokits AD, Indrischek H, Meiler J, Hamm HE, Stadler PF. Tracing the evolution of the heterotrimeric G protein α subunit in Metazoa. BMC Evol Biol 2018; 18:51. [PMID: 29642851 PMCID: PMC5896119 DOI: 10.1186/s12862-018-1147-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2017] [Accepted: 03/06/2018] [Indexed: 01/07/2023] Open
Abstract
BACKGROUND Heterotrimeric G proteins are fundamental signaling proteins composed of three subunits, Gα and a Gβγ dimer. The role of Gα as a molecular switch is critical for transmitting and amplifying intracellular signaling cascades initiated by an activated G protein Coupled Receptor (GPCR). Despite their biochemical and therapeutic importance, the study of G protein evolution has been limited to the scope of a few model organisms. Furthermore, of the five primary Gα subfamilies, the underlying gene structure of only two families has been thoroughly investigated outside of Mammalia evolution. Therefore our understanding of Gα emergence and evolution across phylogeny remains incomplete. RESULTS We have computationally identified the presence and absence of every Gα gene (GNA-) across all major branches of Deuterostomia and evaluated the conservation of the underlying exon-intron structures across these phylogenetic groups. We provide evidence of mutually exclusive exon inclusion through alternative splicing in specific lineages. Variations of splice site conservation and isoforms were found for several paralogs which coincide with conserved, putative motifs of DNA-/RNA-binding proteins. In addition to our curated gene annotations, within Primates, we identified 15 retrotranspositions, many of which have undergone pseudogenization. Most importantly, we find numerous deviations from previous findings regarding the presence and absence of individual GNA- genes, nuanced differences in phyla-specific gene copy numbers, novel paralog duplications and subsequent intron gain and loss events. CONCLUSIONS Our curated annotations allow us to draw more accurate inferences regarding the emergence of all Gα family members across Metazoa and to present a new, updated theory of Gα evolution. Leveraging this, our results are critical for gaining new insights into the co-evolution of the Gα subunit and its many protein binding partners, especially therapeutically relevant G protein - GPCR signaling pathways which radiated in Vertebrata evolution.
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Affiliation(s)
- A. D. Lokits
- 0000 0001 2264 7217grid.152326.1Neuroscience Program, Vanderbilt University, Nashville, TN USA ,0000 0001 2264 7217grid.152326.1Center for Structural Biology, Vanderbilt University, Nashville, TN USA
| | - H. Indrischek
- 0000 0001 2230 9752grid.9647.cBioinformatics Group, Department of Computer Science, Leipzig University, Leipzig, Germany ,0000 0001 2230 9752grid.9647.cComputational EvoDevo Group, Bioinformatics Department, Leipzig University, Leipzig, Germany
| | - J. Meiler
- 0000 0001 2264 7217grid.152326.1Center for Structural Biology, Vanderbilt University, Nashville, TN USA ,0000 0001 2264 7217grid.152326.1Chemistry Department, Vanderbilt University, Nashville, TN USA
| | - H. E. Hamm
- 0000 0004 1936 9916grid.412807.8Pharmacology Department, Vanderbilt University Medical Center, Nashville, TN USA
| | - P. F. Stadler
- 0000 0001 2230 9752grid.9647.cBioinformatics Group, Department of Computer Science, Leipzig University, Leipzig, Germany ,0000 0001 0674 042Xgrid.5254.6Center for non-coding RNA in Technology and Health, University of Copenhagen, Frederiksberg C, Denmark ,0000 0001 2286 1424grid.10420.37Institute for Theoretical Chemistry, University of Vienna, Wien, Austria ,0000 0001 2230 9752grid.9647.cIZBI-Interdisciplinary Center for Bioinformatics and LIFE-Leipzig Research Center for Civilization Diseases and Competence Center for Scalable Data Services and Solutions, University Leipzig, Leipzig, Germany ,grid.419532.8Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany ,0000 0001 1941 1940grid.209665.eSanta Fe Institute, Santa Fe, NM USA
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